Victoria Hewitt
May 2nd, 2010
Math 7D Big Idea: Negative numbers help us to model many real world situations.
Essential Question: How do I multiply and divide integers?
5.3: Using A Calculator To Explore Lines Jean has several profit equations, each based on a different start-up cost. She borrows her brother’s graphing calculator so she can explore the graphs of the equations. Since she has never used the calculator before, she decides to start by experimenting with some simple equations.
Notes:
Graphing Calculator: a calculator capable of plotting 2-dimensional data through graphs and tables, solving simultaneous equations, and performing numerous other tasks with variables.
A. 1. Enter the equation y=4x into your graphing calculator as Y1, and then press GRAPH to see a graph of the equation. Make a sketch of the graph you see.
This is the graph that I see after graphing the equation y=4x with my graphing calculator.
2. Predict how the graph of y=-4x will differ from the graph of y=4x. Then, enter the equation y=-4x as Y2, and press GRAPH to see the graphs of both equations in the same window. Add a sketch of y=-4x to your sketch from part 1.
I think that the equation y=-4x will make a graph that has a straight line starting on the fourth quadrant instead of the third, and passing through the origin [0] to move towards the second quadrant. I think that if you made one graph with both lines from the equations y=4x and y=-4x that they would form an X.
This is how the graph of the equation y=-4x looks like:
3. How are the graphs alike? How are they different?
The graphs, or really lines, are alike because they both pass through 0, they are both straight lines, and neither of them have an exponent of x in their equations. They are different because the graph of y=4x starts from the third quadrant and then goes to the first, and the graph of y=-4x starts at the fourth quadrant and goes to the second quadrant. They are also different because they start on opposite sides of the plane.
B. 1.Press TABLE to look at the table showing data for both equations (y=4x and y=-4x). You may need to use the [non-computable symbol] (looks like the play button on a DVD remote) key to see the Y2column. Copy part of the table onto your paper.
Y = -4x
Y = 4x
2.For each value of x in the table, look at the two corresponding values of y (Y1and Y2). How are the two y values for a given x value related? How does this relationship show up in the graph?
For every value of X up to 0 in the equation y = 4x, the Y value is negative. After 0 they are all positive. It is the opposite with the equation y = -4x. Therefore, on a graph of both of the lines, there is an X made from both of the lines.
C. With your graphing calculator, experiment with each set of equations. Look at the graphs and tables. Record your observations.
1. y=4x + 5 and y=-4x + 5
Both of these equations are opposites. This is very clearly shown in the graph, but you have to look more carefully at the tables to be able to see this relationship. For example, on the graph you see the same kind of line on each side (negative and positive) that relatively moves in the same opposite direction and forms an X type shape. But, in the table the values of Y do not seem to be opposites. But if you look at, for example, the x value of 4 for the first equation, and then the x value of negative 4 for the next, you’ll see that the y outcomes on either side are opposites. For 4 in the first equation, the y value is 21, and for the second equation the -4 has the y value of -21.
2. y=4x – 5 and y=-4x – 5
Both of these equations are also opposites. You can observe the same types of patterns with them on the graph and the table.
May 2nd, 2010
Math 7D
Big Idea: Negative numbers help us to model many real world situations.
Essential Question: How do I multiply and divide integers?
5.3: Using A Calculator To Explore Lines
Jean has several profit equations, each based on a different start-up cost. She borrows her brother’s graphing calculator so she can explore the graphs of the equations. Since she has never used the calculator before, she decides to start by experimenting with some simple equations.
Notes:
Graphing Calculator: a calculator capable of plotting 2-dimensional data through graphs and tables, solving simultaneous equations, and performing numerous other tasks with variables.
A. 1. Enter the equation y=4x into your graphing calculator as Y1, and then press GRAPH to see a graph of the equation. Make a sketch of the graph you see.
This is the graph that I see after graphing the equation y=4x with my graphing calculator.
2. Predict how the graph of y=-4x will differ from the graph of y=4x. Then, enter the equation y=-4x as Y2, and press GRAPH to see the graphs of both equations in the same window. Add a sketch of y=-4x to your sketch from part 1.
I think that the equation y=-4x will make a graph that has a straight line starting on the fourth quadrant instead of the third, and passing through the origin [0] to move towards the second quadrant. I think that if you made one graph with both lines from the equations y=4x and y=-4x that they would form an X.
This is how the graph of the equation y=-4x looks like:
3. How are the graphs alike? How are they different?
The graphs, or really lines, are alike because they both pass through 0, they are both straight lines, and neither of them have an exponent of x in their equations. They are different because the graph of y=4x starts from the third quadrant and then goes to the first, and the graph of y=-4x starts at the fourth quadrant and goes to the second quadrant. They are also different because they start on opposite sides of the plane.
B. 1.Press TABLE to look at the table showing data for both equations (y=4x and y=-4x). You may need to use the [non-computable symbol] (looks like the play button on a DVD remote) key to see the Y2column. Copy part of the table onto your paper.
Y = -4x
Y = 4x
2.For each value of x in the table, look at the two corresponding values of y (Y1and Y2). How are the two y values for a given x value related? How does this relationship show up in the graph?
For every value of X up to 0 in the equation y = 4x, the Y value is negative. After 0 they are all positive. It is the opposite with the equation y = -4x. Therefore, on a graph of both of the lines, there is an X made from both of the lines.
C. With your graphing calculator, experiment with each set of equations. Look at the graphs and tables. Record your observations.
1. y=4x + 5 and y=-4x + 5
Both of these equations are opposites. This is very clearly shown in the graph, but you have to look more carefully at the tables to be able to see this relationship. For example, on the graph you see the same kind of line on each side (negative and positive) that relatively moves in the same opposite direction and forms an X type shape. But, in the table the values of Y do not seem to be opposites. But if you look at, for example, the x value of 4 for the first equation, and then the x value of negative 4 for the next, you’ll see that the y outcomes on either side are opposites. For 4 in the first equation, the y value is 21, and for the second equation the -4 has the y value of -21.
2. y=4x – 5 and y=-4x – 5
Both of these equations are also opposites. You can observe the same types of patterns with them on the graph and the table.